The surplus prior to ruin and the deficit at ruin for a correlated risk process

Badescu, Andrei and Breuer, Lothar and Drekic, Steve and Latouche, Guy
(2005)
The surplus prior to ruin and the deficit at ruin for a correlated risk process.
Scandinavian Actuarial Journal, 2005
(6).
pp. 433-445.
ISSN 1651-2030.
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Abstract

This paper presents an explicit characterization for the joint probability density function of the surplus immediately prior to ruin and the deficit at ruin for a general risk process, which includes the Sparre-Andersen risk model with phase-type inter-claim times and claim sizes. The model can also accommodate a Markovian arrival process which enables claim sizes to be correlated with the inter-claim times. The marginal density function of the surplus immediately prior to ruin is specifically considered. Several numerical examples are presented to illustrate the application of this result.